Carl Friedrich Gauss (1777-1855)

At the age of seven, Carl Friedrich Gauss started elementary
school, and his potential was noticed almost immediately. His teacher, Büttner,
and his assistant, Martin Bartels, were amazed when Gauss summed the integers
from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each
pair summing to 101. In 1795 Gauss left Brunswick to study at Göttingen University.

Gauss's teacher there was Kaestner, whom Gauss often ridiculed. Gauss
left Göttingen in 1798without a diploma, but by this time he had made one of
his most important discoveries - the construction of a regular 17-gon by ruler
and compasses This was the most major advance in this field since the time of
Greek mathematics and was published as Section VII of Gauss's famous work,
Disquisitiones Arithmeticae. Gauss returned to Brunswick where he received a
degree in 1799. After the Duke of Brunswick had agreed to continue Gauss's
stipend, he requested that Gauss submit a doctoral dissertation to the University
of Helmstedt.

Although he did not disclose his methods at the time, Gauss had used his
least squares approximation method. In June 1802 Gauss visited Olbers who had
discovered Pallas in March of that year and Gauss investigated its orbit. Olbers
requested that Gauss be made director of the proposed new observatory in Göttingen,
but no action was taken. Gauss began corresponding with Bessel, whom he did
not meet until 1825, and with Sophie Germain. In 1807 Gauss left Brunswick to take up the position of director of the Göttingen
observatory. Gauss arrived in Göttingen in late 1807. In 1808 his father died,
and a year later Gauss's wife Johanna died after giving birth to their second
son, who was to die soon after her.

Gauss's work never seemed to suffer from his personal tragedy. He published
his second book, Theoria motus corporum coelestium in sectionibus conicis Solem
ambientium, in 1809, a major two volume treatise on the motion of celestial
bodies. In the first volume he discussed differential equations, conic sections
and elliptic orbits, while in the second volume, the main part of the work,
he showed how to estimate and then to refine the estimation of a planet's
orbit.

Gauss had been asked in 1818 to carry out a geodesic survey of the state
of Hanover to link up with the existing Danish grid. Gauss was pleased to accept
and took personal charge of the survey, making measurements during the day and
reducing them at night, using his extraordinary mental capacity for calculations.
He regularly wrote to Schumacher, Olbers and Bessel, reporting on his progress
and discussing problems. Because of the survey, Gauss invented the heliotrope
which worked by reflecting the Sun's rays using a of mirrors and a small
telescope. However, inaccurate base lines were used for the survey and an unsatisfactory
network of triangles.

From the early 1800sGauss had an interest in the question of the possible
existence of a non-Euclidean geometry. He discussed this topic at length with
Farkas Bolyai and in his correspondence with Gerling and Schumacher. In a book
review in 1816he discussed proofs which deduced the axiom of parallels from
the other Euclidean axioms, suggesting that he believed in the existence of
non-Euclidean geometry, although he was rather vague.

The period 1817-1832 was a particularly distressing time for Gauss. He took
in his sick mother in 1817, who stayed until her death in 1839, while he was
arguing with his wife and her family about whether they should go to Berlin.
He had been offered a position at Berlin University and Minna and her family
were keen to move there. Gauss, however, never liked change and decided to stay
in Göttingen. In 1831 Gauss's second wife died after a long illness. In
1831, Wilhelm Weber arrived in Göttingen as physics professor filling Tobias
Mayer's chair. Gauss had known Weber since 1828 and supported his appointment.

In 1832, Gauss and Weber began investigating the theory of terrestrial magnetism
after Alexander von Humboldt attempted to obtain Gauss's assistance in making
a grid of magnetic observation points around the Earth. Gauss was excited by
this prospect and by 1840 he had written three important papers on the subject:
Intensitas vis magneticae terrestris ad mensuram absolutam revocata (1832),
Allgemeine Theorie des Erdmagnetismus (1839) and Allgemeine Lehrsätze in Beziehung
auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungs-
und Abstossungskräfte (1840).

These papers all dealt with the current theories on terrestrial magnetism,
including Poisson's ideas, absolute measure for magnetic force and an empirical
definition of terrestrial magnetism. Dirichlet's principle was mentioned
without proof. Allgemeine Theorie... showed that there can only be two poles
in the globe and went on to prove an important theorem, which concerned the
determination of the intensity of the horizontal component of the magnetic force
along with the angle of inclination. Gauss used the Laplace equation to aid
him with his calculations, and ended up specifying a location for the magnetic
South pole.

Humboldt had devised a calendar for observations of magnetic declination.
However, once Gauss's new magnetic observatory (completed in 1833- free
of all magnetic metals) had been built, he proceeded to alter many of Humboldt's
procedures, not pleasing Humboldt greatly. However, Gauss's changes obtained
more accurate results with less effort. Gauss and Weber achieved much in their
six years together. They discovered Kirchhoff's laws, as well as building
a primitive telegraph device which could send messages over a distance of 5000
ft. However, this was just an enjoyable pastime for Gauss.

He was more interested in the task of establishing a world-wide net of magnetic
observation points. This occupation produced many concrete results. The Magnetischer
Verein and its journal were founded, and the atlas of geomagnetism was published,
while Gauss and Weber's own journal in which their results were published
ran from 1836 to 1841. In 1837, Weber was forced to leave Göttingen when he
became involved in a political dispute and, from this time, Gauss's activity
gradually decreased. He still produced letters in response to fellow scientists'
discoveries usually remarking that he had known the methods for years but had
never felt the need to publish. Sometimes he seemed extremely pleased with advances
made by other mathematicians, particularly that of Eisenstein and of Lobachevsky.